Let G be a connected reductive algebraic group. We develop a Gröbner theory for multiplicity-free G-algebras, as well as a tropical geometry for subschemes in a spherical homogeneous space G/H. We define the notion of a spherical tropical variety and prove a fundamental theorem of tropical geometry in this context. We also propose a definition for a spherical amoeba in G/H using Cartan decomposition. Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.
|Number of pages||51|
|State||Published - Dec 1 2019|
Bibliographical notePublisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology